Locally Symmetric Homogeneous Finsler Spaces

Let (M,F) be a connected Finsler space and d the distance function of (M,F). A Clifford translation is an isometry ρ of (M,F) of constant displacement, in other words such that d(x,ρ(x)) is a constant function on M. In this paper, we consider a connected simply connected symmetric Finsler space and a discrete subgroup Γ of the full group of isometries. We prove that the quotient manifold (M,F)/Γ is a homogeneous Finsler space if and only if Γ consists of Clifford translations of (M,F). In the process of the proof of the main theorem, we classify all the Clifford translations of symmetric Finsler spaces.